Marcello M. Bonsangue

CONCEPTS FOR MODELING ENTERPRISE ARCHITECTURES

A coherent description of enterprise architecture provides insight, enables communication among stakeholders and guides complicated change processes. Unfortunately, so far no enterprise architectur...

Generalized metric spaces: completion, topology, and power domains via the Yoneda embedding

Abstract Generalized metric spaces are a common generalization of preorders and ordinary metric spaces (Lawvere, 1973). Combining Lawveres (1973) enriched-categorical and Smyths (1988, 1991) topological view on generalized metric spaces, it is shown how to construct 1. (1) completion, 2. (2)two topologies, and 3. (3) powerdomains for generalized metric spaces. Restricted to the special cases of preorders and ordinary metric spaces, these constructions yield, respectively: 1. (1) chain completion and Cauchy completion; 2. (2) the Alexandroff and the Scott topology, and the e-ball topology; 3. (3) lower, upper, and convex powerdomains, and the hyperspace of compact subsets. All constructions are formulated in terms of (a metric version of) the Yoneda (1954) embedding.

Towards a language for coherent enterprise architecture descriptions

A coherent description of architectures provides insight, enables communication among different stakeholders and guides complicated (business and ICT) change processes. Unfortunately, so far no architecture description language exists that fully enables integrated enterprise modeling. In this paper we focus on the requirements and design of such a language. This language defines generic, organization-independent concepts that can be specialized or composed to obtain more specific concepts to be used within a particular organisation. It is not our intention to re-invent the wheel for each architectural domain: wherever possible we conform to existing languages or standards such as UML. We complement them with missing concepts, focusing on concepts to model the relationships among architectural domains. The concepts should also make it possible to define links between models in other languages. The relationship between architecture descriptions at the business layer and at the application layer (business-IT alignment) plays a central role.

Generalizing Determinization from Automata to Coalgebras

The powerset construction is a standard method for converting a nondeter- ministic automaton into a deterministic one recognizing the same language. In this paper, we lift the powerset construction from automata to the more general framework of coal- gebras with structured state spaces. Coalgebra is an abstract framework for the uniform study of different kinds of dynamical systems. An endofunctor F determines both the type of systems (F-coalgebras) and a notion of behavioural equivalence (�F) amongst them. Many types of transition systems and their equivalences can be captured by a functor F. For example, for deterministic automata the derived equivalence is language equivalence, while for non-deterministic automata it is ordinary bisimilarity. We give several examples of applications of our generalized determinization construc- tion, including partial Mealy machines, (structured) Moore automata, Rabin probabilistic automata, and, somewhat surprisingly, even pushdown automata. To further witness the generality of the approach we show how to characterize coalgebraically several equivalences which have been object of interest in the concurrency community, such as failure or ready semantics.

Change impact analysis of enterprise architectures

An enterprise architecture is a high-level description intended to capture the vision of an enterprise integrating all its dimensions: organization structure, business processes, and infrastructure. Every single part of an enterprise is subject to change, and each change may have significant consequences within all domains of the enterprise. A lot of effort is therefore devoted to maintaining the integrity of an architectural description. In this paper we address the problem of mastering the ripple effects of a proposed change. This allows architects to assess the consequences of a particular change to the enterprise, in order to identify potential impacts of a change before it actually takes place.

Duality for logics of transition systems

We present a general framework for logics of transition systems based on Stone duality. Transition systems are modelled as coalgebras for a functor T on a category χ. The propositional logic used to reason about state spaces from χ is modelled by the Stone dual

An Approach to Object-Orientation in Action Systems

{\mathcal A}

Generalizing the powerset construction, coalgebraically

of χ (e.g. if χ is Stone spaces then

Sound and Complete Axiomatizations of Coalgebraic Language Equivalence

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Algebra-coalgebra duality in brzozowski's minimization algorithm

is Boolean algebras and the propositional logic is the classical one). In order to obtain a modal logic for transition systems (i.e. for T-coalgebras) we consider the functor L on